Thanks to Wraith10 for this infomation.
Berries
You can find berries growing on plants or obtain them in various other ways. See the item list for locations of specific berries.You can also use thief or covet to steal berries, especially well in the battle tower where you can steal rare berries. However you will only be able to keep them until the battle is over. There are also some special people to get berries from:
Two Berries a day from Kiri (Sootopolis - below gym on left side): figy, iapapa, pomeg, kelpsy, qualot, hondew, grepa, tamato, cornn, magost, rabuta, nomel

Berry Master's house on route 123:
Husband (2 per day): pomeg, kelpsy, qualot, hondew, grepa, tamato, cornn, magost, rabuta, nomel
Wife: She makes you play a game to get berries the key is as follows:

The more common berries can be gotten through numerous different sayings, and which of the common berries you get varies so there is no exact science to it. An example of this is Angry Abra, which can net you an Oran, Lum, or Sitrus berry reportedly, and perhaps others.

Additionally you can plant a berry in a dirt patch and it will grow into a plant with many more such berries on it. If you use the Wailmer Pail to water berries they will produce more and faster. This is vital for low yield rare berries. Water often!
Berry Growing Times:
All times given are in hours
Sprouts: Time it takes the berry to sprout
Grows: Time it takes berry to grow
Blooms: Time it takes berry to bloom
Ready: Time the berry can be picked

You can now enter your pokemon in contests to compete in five new categories; cool, beauty, cute, smart, tough. You will compete against three pokemon. There are four levels of competition; normal, super, hyper, and master. Each contest emphasizes certain elements as well as a pokemon's luster. You can check a pokemon's condition in the pokenav, it will also indicate a pokemon's luster with shine.

To enter your first contest you have to go to Verdanturf City and talk to the lady behind the counter in the pokemon contest center. She will explain the rules to you and give you the contest pass.

Main Judging
The audience will judge the four competing pokemon and the judge records which pokemon receives the most applause. Applause is shown by hearts. It is good to have a strong luster and high rating in the condition you are competing in. Use pokeblocks to raise the condition you wish.

Round Judging
In five rounds you will try to appeal more to the audience than your competitors. Each move your pokemon knows will have a different effect in the contest. You can even make combos for extra appeal. Turn order is decided by your scores in each previous round. Hearts are worth 10 points each, you can also deliver Jam hearts that take off 10 points each. The player with the most points wins. Originality will give you more points, copying will earn you less. You can use defensive moves to prevent your opponents from interfering with you, try to interfere with an opponent, or go with a move to earn as many points as you can. If you win there will be a shower of confetti and then you can claim your prize ribbon from the judges.

Symbol Explanation
Hearts (red or white): Appeal points. Give you 10 points each.
Hearts (black): Jam points. Take off 10 points each.
Stars: Also worth 10 points each.
Numbers: Indicate turn order for next round.
Question Mark: Indicates random turn order for next round.
Exclamation Marks: Indicates which moves can begin a combo (moves to finish a combo are highlighted in red)
Circles: Prevent the loss of hearts.
Grey highlighting: Shows the move you used last round
Red highlighting: See Exclamation Marks
Spiral: Lose points for repeating a move, crowd excitement decreases
X: Lose a turn as a result of a move you did
Wavy Line: Lose a turn as a result of a move someone else performed
Ear: You are affected by a jam and lose points

Bonuses
Crowd Excitement: If the crowd excitement reaches the max (5 degrees) on your turn you earn 60 points.
Type Bonus: Use an appeal move that matches the type of contest it is to earn an extra 10 points.
Combo Bonus: Execute a move then on the next turn execute a complimentary move.
Condition Bonus: Some moves will earn you a star, worth 10 points

Attached Items
There are 5 kinds of scarfs that when attached to a pokemon make it do better in the corresponding contest.

A Special Prize
Every time you win a pokemon contest and get your picture painted ask for it to be donated to the art gallery. After you fill the second floor (win all contests at master level) you willl receive the glass ornament from the art director.

Level: The higher the quality level, the more it will increase the pokemon's condition
Taste: A pokemon benefits most from eating pokeblocks that it likes the flavor of
Feel: More people blending make smoother pokeblocks. Feed the smoothest ones to your pokemon.

Pokeblock Variations: It appears that pokeblocks (like grey, black, and white) which are composted of more than one flavor or raise more than one stat can vary. Because of this chart data on such multiflavored pokeblocks can not be guaranteed to be 100% accurate in all cases. Your best bet is to experiment or choose single flavor pokeblocks.

Collect berries that have the flavors you desire for your pokeblock. You must have the pokeblock case (Slateport City) to use the berry blender. You must then find a berry blender, these are located at the pokemon contest halls. You select what berry to use and then the machine starts. When the blender starts hit A when the pointer reaches your name. Hit it at the right time to accelerate the blender and turn out better berries. If you see a red circle appear you hit it and the blender speeds up. If you see a red circle within a red circle it was perfect and it speeds up even more. A blue X shows you missed and the machine slows down. Once the machine has finished mixing the pokeblock it goes into your pokeblock case where you can use it later.

There are 15 colors of pokeblocks in all: Red, Blue, Pink, Green, Yellow, Purple, Indigo, Brown, LiteBlue, Olive, Grey, Black, White, and Gold. Depending on their natures pokemon prefer different flavours of pokeblocks. They however cannot eat an unlimited amount and eventually they will reach a saturation point where you cannot feed them any more.

Master Rank Result
Persim Not a brown pokeblock Sour/Sweet Not a brown pokeblock
Sitrus Not a brown pokeblock Not a brown pokeblock Sour/Sweet
Nanab Bitter/Swett Sour/Sweet Not a brown pokeblock
Pinap Not a brown pokeblock Not a brown pokeblock Sour/Sweet
Qualot Spicy/Sweet Not a brown pokeblock Not a brown pokeblock
Grepa Not a brown pokeblock Not a brown pokeblock Sour/Sweet
Magost Bitter/Sweet Sour/Sweet Spicy/Sweet

Master Rank Result
Pomeg Not a gray pokeblock Spicy/Bitter/Sweet Not a gray pokeblock
Kelpsy Not a gray pokeblock Bitter/Dry/Sour Not a gray pokeblock
Qualot Not a gray pokeblock Spicy/Sour/Sweet Not a gray pokeblock
Hondew Not a gray pokeblock Spicy/Bitter/Dry Not a gray pokeblock
Grepa Not a gray pokeblock Dry/Sour/Sweet Not a gray pokeblock